Details

analyze2.8s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

sample434.0ms

Algorithm

intervals

Results

350.0ms	151×	body	1280	valid
49.0ms	69×	body	640	valid
13.0ms	25×	body	320	valid
3.0ms	8×	body	160	valid
0.0ms	3×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	95	19
1	95	19

prune23.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 17.4b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
4.2b	(cos (- lambda1 lambda2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `cos-sum` `sin-mult`

Counts

4 → 54

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
4.0ms	(cos (- lambda1 lambda2))

series45.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (sin phi2))
24.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))) R)
7.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
5.0ms	(cos (- lambda1 lambda2))

simplify59.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4943	876
1	4943	876

prune171.0ms

Filtered

49 candidates to 66 candidates (-34.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	52	14	66
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	54	14	68

Merged error: 2.7b

Counts

68 → 14

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 64

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
5.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (sin phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
42.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
12.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5166	1173

prune190.0ms

Filtered

51 candidates to 76 candidates (-49.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	63	13	76
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	75	15	90

Merged error: 2.6b

Counts

90 → 15

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
0.8b	(acos (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
2.4b	(log (pow (exp (sin phi1)) (sin phi2)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log`
8×	`pow1` `add-cbrt-cube`
7×	`log-prod`
6×	`associate-r` `associate-l`
4×	`add-log-exp`
3×	`unpow-prod-down` `rem-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `pow-to-exp` `pow-exp` `log-pow` `sin-mult` `sqr-pow`

Counts

4 → 63

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(* (acos (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
2.0ms	(acos (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
3.0ms	(log (pow (exp (sin phi1)) (sin phi2)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (sin lambda2))
48.0ms	(* (acos (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
13.0ms	(acos (+ (log (pow (exp (sin phi1)) (sin phi2))) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
22.0ms	(log (pow (exp (sin phi1)) (sin phi2)))

simplify45.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4957	1204
1	4957	1204

prune162.0ms

Filtered

45 candidates to 75 candidates (-66.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	75	15	90

Merged error: 2.6b

Counts

90 → 15

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))) R)
0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))))
26.7b	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `sin-mult` `rem-cube-cbrt` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `pow1/3` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))) R)
5.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))))
3.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series80.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))) R)
18.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
12.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))))
9.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify36.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4897	1250
1	4897	1250

prune96.0ms

Filtered

54 candidates to 79 candidates (-46.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	79	15	94

Merged error: 2.6b

Counts

94 → 15

regimes1.2s

Accuracy

0% (0.3b remaining)

Error of 3.8b against oracle of 3.5b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	28
1	31	28

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.1s	4701×	body	1280	valid
1.6s	2177×	body	640	valid
350.0ms	711×	body	320	valid
84.0ms	263×	body	160	valid
34.0ms	10×	body	2560	valid
23.0ms	138×	body	80	valid
1.0ms	1×	body	1280	invalid
1.0ms	2×	body	320	invalid

Details

analyze2.8s

sample434.0ms

simplify5.0ms

prune23.0ms

localize25.0ms

rewrite14.0ms

series45.0ms

simplify59.0ms

prune171.0ms

localize31.0ms

rewrite15.0ms

series72.0ms

simplify47.0ms

prune190.0ms

localize39.0ms

rewrite15.0ms

series93.0ms

simplify45.0ms

prune162.0ms

localize34.0ms

rewrite14.0ms

series80.0ms

simplify36.0ms

prune96.0ms

regimes1.2s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.6s

Profiling